If the surface figures of the substrates do not match precisely, bonding could be improved by including a filling material in the bonding solution. The filling material could be in the form of particles, foam, and/or a liquid. The filling material facilitates bridging of gaps between the substrate surfaces. Preferably, the filling material should include at least one ingredient that can be hydrated to have exposed hydroxyl groups and that can be chemically linked, by hydroxide catalysis, to a silicatelike network. The silicatelike network could be generated in situ from the filling material and/or substrate material, or could be originally present in the bonding material.